Energy formulae for two-particle Klein-Gordon systems subjected to Coulomb and Yukawa potentials are derived to first 1/ N -order. The energies obtained in this manner incorporate the influence of the mass-asymmetry via the parameter δ = ( m 1 2 − m 2 2 ) 2 . Certain Coulomb-inspired extrapolations to Dirac-particle systems, having the meaning of dominant contributions, are taken into account. Numerical results are presented.